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Global bifurcation mechanism and local stability of identical and equidistant regions

José Gaspar (), Kiyohiro Ikeda () and Mikihasa Onda ()
Additional contact information
Kiyohiro Ikeda: Department of Civil and Environmental Engineering, Tohoku University
Mikihasa Onda: Department of Civil and Environmental Engineering, Tohoku University

No 4, Working Papers de Economia (Economics Working Papers) from Católica Porto Business School, Universidade Católica Portuguesa

Abstract: We provide an analytical description of possible spatial patterns in economic geography models with three identical and equidistant regions by applying results from General Bifurcation mechanisms. We then use Pflüger’s (2004, Reg Sci UrbEcon) model to show what spatial patterns can be uncovered analytically. As the freeness of trade increases, a uniform distribution undergoes a direct bifurcation that leads to a state with two identical large regions and one small region. Before this bifurcation, the model encounters a minimum point above which a curve of dual equilibria with two small identical regions and one small region emerges. From further bifurcations, the equilibrium with one large region encounters agglomeration in a single region, while the equilibrium with one small region encounters a state with two evenly populated regions and one empty region. A secondary bifurcation then leads to partial agglomeration with one small region and one large region. We show that an asymmetric equilibrium h populated regions cannot be connected with other types of equilibria. Therefore, an initially asymmetric state will remain so and preserve the ordering between region sizes.

Keywords: bifurcation; economic geography; multi-regional economy; footloose entrepreneur (search for similar items in EconPapers)
JEL-codes: R10 R12 R23 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2019-07
New Economics Papers: this item is included in nep-geo and nep-ure
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Persistent link: https://EconPapers.repec.org/RePEc:cap:wpaper:042019

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